Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model

Abstract

Recent studies on the Lorentzian version of the type IIB matrix model show that (3+1)D expanding universe emerges dynamically from (9+1)D space-time predicted by superstring theory. Here we study a bosonic matrix model obtained by omitting the fermionic matrices. With the adopted simplification and the usage of a large-scale parallel computer, we are able to perform Monte Carlo calculations with matrix size up to $N=512$, which is twenty times larger than that used previously for the studies of the original model. When the matrix size is larger than some critical value $N_{\mathrm{c}}\simeq 110$, we find that (3+1)D expanding universe emerges dynamically with a clear large-$N$ scaling property. Furthermore, at sufficiently late times, we observe a power-law behavior $t^{1/2}$ of the spatial extent with respect to time $t$, which is reminiscent of the expanding behavior of the Friedmann-Robertson-Walker universe in the radiation dominated era. We discuss possible implications of this result on the original model including fermionic matrices.

22 pages, 21 figures, 4 tables, (v2) typos corrected

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• Complex Langevin analysis of the spontaneous symmetry breaking in dimensionally reduced super Yang-Mills models
• Measuring finite Quantum Geometries via Quasi-Coherent States
• Progress in the numerical studies of the type IIB matrix model
• Emergent Metric Space-Time from Matrix Theory
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• The emergence of expanding space-time and intersecting D-branes from classical solutions in the Lorentzian type IIB matrix model
• Kähler structure in the commutative limit of matrix geometry
• On the structure of the emergent 3d expanding space in the Lorentzian type IIB matrix model
• Universality and the dynamical space-time dimensionality in the Lorentzian type IIB matrix model